Characteristic lengths catalytic pellets

What is the critical value of the intrapeUet Damkohler number for onedimensional diffusion and zeroth-order irreversible chemical reaction in catalytic pellets with spherical symmetry The radius of the sphere is used as the characteristic length in flie definition of the Damkohler number. 

Step 12. Calculate the intrapellet Damkohler number, where the characteristic length is the radius of the catalytic pellet. 

The appropriate diffusion coefficient of reactant A2 must be modified by intrapellet porosity and tortuosity factors which summarize the internal pore structure of each catalytic pellet. For spherical catalysts, the peUet radius R is taken as the characteristic length L. 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

There are however some particularities when the effectiveness of a catalytic coating is considered. First, the length scale for internal diffusion (t ) is typically much smaller than the one for external transport (a), as shown in Figure 8.1. The ratio between these characteristic distances governs the coating curvature. Second, the area available for diffusion increases as the reactant penetrates in the catalytic body and is maximum at the interface with the impermeable/symmetry boundary. The latter characteristic only requires minor adaptations, if any. The former feature can be also found in e shell particles, which can be thought of as a catalytic coating on a (possibly, spherical) pellet. The similarity between the effectiveness of coated channels and particles was addressed in Lopes et al. [94]. 

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